SPHERES AND CYLINDERS 



133 



FIG. 99 



221. Find the thickness necessary to give to a steel locomotive cylinder of 22 in. 

 internal diameter if it is required to withstand a maximum steam pressure of 

 1501b./in. 2 with a factor of safety of 10, using both Lamp's and Clavarino's formulas. 



222. In a four-cycle gas engine the cylinder is of steel 

 with an internal diameter of 6 in., and the initial internal 

 pressure is 200 lb./in. 2 absolute. With a factor of safety 

 of 15, how thick should the walls of the cylinder be made, 

 according to Lamp's formula ? 



223. The steel cylinder of a hydraulic press has an 

 internal diameter of 5 in. and an external diameter of 7 in. 

 With a factor of safety of 3, how great an internal pressure 

 can the cylinder withstand, according to Lamp's formula ? 



224. In a fire-tube boiler the tubes are of drawn steel, 

 2 in. internal diameter and J in. thick. What is the factor 

 of safety for a working gauge pressure of 200 lb./in. 2 ? 



225. How great is the stress in a copper sphere 2 ft. in 

 diameter and .25 in. thick under an internal pressure of 

 175 lb./in. 2 ? 



226. A cast-iron water pipe is 24 in. in diameter and 

 2 in. thick. What is the greatest internal pressure which it 

 can withstand, according to the formula for thin cylinders ? 



227. A wrought-iron cylinder is 8 in. in external diame- 

 ter and 1^ in. thick. How great an external pressure can 

 it withstand ? 



228. An elevated water tank is cylindrical in form, with 



a hemispherical bottom (Fig. 99). The diameter of the tank is 20 ft. and its height 

 52 ft. (exclusive of the bottom). If the tank is to be built of wrought iron and the 

 factor of safety is taken to be 6, what should be the thickness of the bottom plates 

 and also of those in the body of the tank near its bottom ? 



NOTE. Formulas (165) and (166) give the required thick- 

 ness of the plates, provided the tank is without joints. The 

 bearing power of the rivets at the joints, however, is, in general, 

 the consideration which determines the thickness of the plates 

 (article 90). 



229. A marine boiler shell is 16 ft. long, 8 ft. in diam- 

 eter, and 1 in. thick. What is the stress in the shell for a 

 working gauge pressure of 160 lb./in. 2 ? 



230. The air chamber of a pump is made of cast iron 

 of the form shown in Fig. 100. If the diameter of the air 

 chamber is 10 in. and its height 24 in., how thick must the 

 walls of the air chamber be made in order to stand a pres- 

 sure of 500 lb./in. 2 , with a factor of safety of 4 ? 



231. The end plates of a boiler shell are curved out to 

 a radius of 5 ft. If the plates are f in. thick, find the tensile 

 stress due to a steam pressure of 175 lb./in. 2 



232. If the thickness of the end plates in problem 231 



is changed to ^ in., the steam pressure being the same, to what radius should 

 they be curved in order that the tensile stress in them shall remain the same ? 



FIG. 100 



